1. (a) Let X follow an exponential distribution with parameter 1 =1. Denote the mean value and variance of X by u = 1 an

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1 A Let X Follow An Exponential Distribution With Parameter 1 1 Denote The Mean Value And Variance Of X By U 1 An 1 (34.53 KiB) Viewed 78 times

1. (a) Let X follow an exponential distribution with parameter 1 =1. Denote the mean value and variance of X by u = 1 and o2 = 1 respectively. i. Compute the approximate expectation of X3 using the 2nd order moment approximation Elo(X)] − o(u) + 10"()o2 with $(x) = x3. Sketch the graph of o as well as the approximating function obtained from 2nd order Taylor approximation about h, i.e. about x = 1. [4] ii. Compute E[X3] exactly, e.g. by integration or by using the mgf. (TYPE:) Discuss the direction of the deviation of the approximation computed above from the true value. [3]